Tagged Questions

This covers all transformations of functions by integrals, including but not limited to the Radon, X-Ray, Hilbert, Mellin transforms. Use (wavelet-transform), (laplace-transform) for those respective transforms, and use (fourier-analysis) for questions about the Fourier and Fourier-sine/cosine ...

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Integral transforms involving logarithms?

We have the fourier-transform: $$F\{f\}(w) = \int_{-\infty}^\infty f(x)\exp(iwx)dx$$ Which has extremely many applications and interpretations throughout science and engineering. For instance since ...
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Conditions under which a convolution transformation is injective in the 1-d Torus

Let $X=[0,1)$ the 1-d torus. Given a bounded positive function $w\colon X\to\mathbb{R}$ with unit integral (I mean $w\geq 0$, $w\in L^\infty(X)$ and $\int_X w\; dx=1$), define \begin{align*} T_{w} ...
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What are the different type of Daubechies Wavelet transform?

Like Daub4 are there others named as Daub2, daub3 or we only have daub4 , daub8, daub16? What is the order of a transform(represented usually by N)? Does this order have any resemblance with the ...
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Is it possible to define a hankel transform for a function depending of a complex variable

Hankel transform is defined by $F_{\nu}(k) = \int_0^{\infty}f(r)J_{\nu}(kr)rdr$, and the inverse transform by $f(r) = \int_0^{\infty}F_{\nu}(k)J_{\nu}(kr)kdk$, In my problem, r is a complex ...
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Solving 2nd order linear ODE with integral transformation

I have this differential equation $-u''(x)+\mu \cdot u(x)=f(x)$ where $x \in (0,\pi)$ with boundary conditions $u'(0)=u'(\pi)=0$ where $c$ is a constant. I checked the values of $\mu$ where I have ...
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How would you solve this surface integral?

Suppose you had the surface integral $\iint \limits_{A} = x^{3}(1-x^{4}-y^{4})dx \ dy$ where $A$ is the region defined by $x \geq 0, \; y \geq 0, \; x^{4}+y^{4} \leq 1$. How would you solve this ...
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Fourier transforms and Dirac delta function

What is the Dirac delta function $\delta(t_1-t_2)$ in Fourier (frequency) space?
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